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A multilevel event history analysis of the effects of grandmothers on child mortality in a historical German population (Krummhörn, Ostfriesland, 1720-1874)
MPIDR WORKING PAPER WP 2002-023MAY 2002
Jan Beise ([email protected]) Eckart Voland ([email protected])
A multilevel event history analysis of the effects of grandmothers
on child mortality in a historical German population
(Krummhörn, Ostfriesland, 1720-1874)
Jan Beise1,3 and Eckart Voland2
1 Max-Planck-Institute for Demographic ResearchDoberaner Strasse 114, D-18057 Rostock, Germany
phone: (+)49-(0)381-2081-148fax: (+)49-(0)381-2081-448
2 Zentrum für Philosophie und Grundlagen der Wissenschaft, Universität Giessen,Otto-Behaghel-Strasse 10C, D-35394 Giessen, Germany
3 to whom correspondence should be addressed
Abstract
We analyzed data from the historic population of the Krummhörn (Ostfriesland, Germany,
1720-1874) to determine the effects of grandparents in general and grandmothers in particular
on child mortality. Multilevel event-history models were used to test how the survival of
grandparents in general influenced the survival of the children. Random effects were included
in some models in order to take the potentially influential effect of unobserved heterogeneity
into account. It could be shown that while maternal grandmothers indeed improved the child’s
survival, paternal grandmothers worsened it. Both grandfathers had no effect. These findings
are not only in accordance with the assumptions of the “grandmother hypothesis” but also
may be interpreted as hints for differential grandparental investment strategies.
1 Introduction
Human life span and especially the long post-reproductive life span in women has drawn
more and more attention during the last years, both by demographers interested in longevity
(Wachter and Finch 1997 and there within Austad) and by evolutionary anthropologists
interested in the evolution of human life-history traits (Hawkes et al. 1998; Hill and Kaplan
1999; Kaplan et al. 2000). Demographers are mainly interested in the causes that have lead
and are still leading to an extension of the average human life span over the course of the last
few hundred years and its consequences for the society both in terms of political and social
changes (Oeppen and Vaupel 2002). In contrast, evolutionary anthropologists consider human
longevity as a specific life history trait (Stearns 1992) and are interested in its evolutionary
history (Hill 1993; Hawkes et al. 1998). Besides the comparatively long life span in general, it
is the extraordinary long postreproductive part in women which demands an evolutionary
explanation (Kaplan 1997; Hawkes et al. 1998). Recent theoretical development in this field
see kin support - especially provided by elder women – as one key factor for the explanation
of one or even both of these human life history traits (Hill 1993; Hawkes et al. 1998;
O’Connell, Hawkes, and Blurton Jones 1999).
The two features longevity and postreproductive life span are interrelated with the occurrence
of a complete cessation of reproductive capabilities - namely, menopause - in women.
Evolutionary-thinking biologists were initially puzzled about the very existence of female
menopause since it occurs relatively early in life and leaves women with decades – not merely
years - of postreproductive life span. Even women living in traditional hunter-gatherer
conditions have on average a remaining life span of about twenty years after they have
experienced menopause (Hill and Hurtado 1996:427). Furthermore, in general, most of those
remaining years may be spent in a relatively healthy state. As Hill and Hurtado (1991: figure
1) showed, the decline of fertility occurs long before and at a much higher rate than any other
physiological trait. Although recent studies show that humans are not the only species that
show a substantial remaining life-span after the cessation of reproductive capabilities (Packer
et al. 1998; see also Austad 1997) they are one of the few higher order taxa and they are
probably the only primates who show this feature regularly and in “non-provisioned”
conditions (Pavelka and Fedigan 1991; Caro et al. 1995; Judge and Carey 2000).
The paradox about human female menopause is that evolutionary theory predicts that there
should be no selection for any post-reproductive life-span. The reason is that sterility is – in
principle - the selective equivalent of death (Williams 1957). Traits which are expressed only
after the end of reproduction are said to be in a “selection shadow”. Post-reproductive life-
span may be seen as such a trait in itself since it requires lasting efforts to keep the body
functioning in a proper way – efforts which could have been invested instead in reproductive
events.
A possible solution to this paradox was first proposed by George Williams in his seminal
paper about the evolution of senescence (1957), which was later labeled the “grandmother
hypothesis” (by Hill and Hurtado 1991; for recent reviews concerning the grandmother
hypothesis see: Hawkes et al. 1998; Peccei 2001a,b; Shanley & Kirkwood 2001). The paradox
is solved if one recognizes that being sterile does not necessarily mean being post-
reproductive in a broader sense. After menopause, women are definitely sterile but – in a
biological fitness sense – they do not have to be post-reproductive. Being reproductive need
not only mean giving birth to a child but may also include rearing and supporting them. Thus,
sterile women may still achieve fitness benefits by increasing survival and fertility of their
offspring or other relatives.
Empirical studies analyzing the helping behavior of grandmothers are not very numerous. Hill
and Hurtado (1996: Chapter 13) found a positive though not significant association for the
Ache population of Paraguay between the presence of both grandmothers and grandfathers
and the survival of their grandchildren. They found no relationship concerning the female
fertility rate. Hawkes et al. (1997) studied the time allocation and offspring provisioning of
the Hadzas in Tanzania and found a positive correlation between grandmaternal foraging time
and children’s weight changes. This last effect was especially strong for the youngest weaned
children of nursing mothers.
Just recently, Sear and colleagues studied the effects of kin on child nutritional status (2000)
and on mortality (2002) in a rural population in Gambia. They found that from all
grandparents, only the maternal grandmother had a positive influence on the child’s situation
concerning both nutritional status and survival (there was actually an increased risk of the
child dying when the maternal grandmother died). The survival effect was only apparent
during the ages of toddlerhood (12-23 months), but not during infancy (0-11 months) and not
in later childhood (22-59 months).
This study analyzes the effect of grandmothers on child mortality in the historic population of
Krummhörn in northern Germany (1720-1874). In a previous study Voland and Beise (2002)
found a slight positive effect on the parity progression probability of woman if both their own
mother and their mother-in-law were alive compared to woman for whom these two were
dead. Furthermore, using a simple transition rate model, they found significant effects of the
grandmothers on the survival of the children. Surprisingly, the effects differed in direction
conditional on whether the grandmother was related maternally or paternally: maternal
grandmothers increased the survival of the children, paternal grandmothers decreased it.
Figure 1 displays Kaplan-Meier survivor functions for children according to the survival
status of their grandmothers. Those children of whom only the maternal grandmother was
alive (at the time of their birth) had the highest survival. Children whose grandmothers were
both still alive had a slightly lower survival. The children who had only a paternal
grandmother had the lowest survival – their survival was even lower than those without a
living grandmother.
[FIGURE 1 ABOUT HERE]
In the following analysis the pattern of the grandmaternal effect on child mortality will be
studied using more appropriate event-history models. First, multi level transition rate models
will be applied in order to account for the fact that many mothers have contributed several
children to the analysis (which may violate assumptions about the independency of
observations which usual regression models assume). Furthermore, data from historical
populations are usually quite limited concerning the information that is available. Therefore, it
can be assumed that unobserved heterogeneity may play an important role in analysis using
those data. In order to have some control for this kind of heterogeneity, random effects will be
included in some of the models.
2 Data
The data derive from a family reconstitution study based on church registers, as well as on tax
rolls and other records of the Krummhörn region (Ostfriesland [East Frisia], Germany, from
the 18th and 19th centuries). Methods of family reconstitution studies and their usage in
historical demography are discussed in Voland (2000a). At present, data collection for 19 of
the 32 parishes in this region is completed. Although a few parish registers had been kept
since the 17th century, data could not be considered reliable until the 18th century, when partial
under-registration (especially of stillbirths and children who died young) could be ruled out.
At present the vital and some social data from slightly more than 23,000 families are
available. A summary of some of the main results of the Krummhörn study is given in Voland
(1990, 1995).
The Krummhörn region is characterized by a very fertile marsh soil. In contrast to the
neighboring heathland and moor regions, large and medium-sized businesses dominated the
farming economy. A capital and market-oriented agriculture developed and then was
replaced by a pure subsistence economy earlier than elsewhere in Germany. Accumulation of
returns was possible and indeed led to remarkable wealth concentration in some lineages.
Consequently, a “two-class society” developed with big farmers who owned both the land and
the capital on the one hand, and a large mass of landless workers and propertyless rural
craftsmen on the other. This division of society is also reflected in reproductive strategies.
While the relatively prosperous farmers manipulated the fates of their children in accordance
with the logic of a resource competition scenario (Voland and Dunbar 1995; Beise 2001), the
mass of workers dealt with fertility “opportunistically”, i.e. the sex of the children and the
family size already attained played practically no role in their investment decisions at any
time. As a result infant mortality did not show any remarkable variance with sex or birth order
for the workers in contrast to the farmers. This is why only the worker families were selected
as a sample for this study. Doing this we avoid any possible grandmother effects that could be
overshadowed by economically motivated investment decisions.
For further details about the socio-cultural background of the Krummhörn see Engel (1990)
and Beise (2001) and the related references therein.
Sample preparation and selection
Historical data sets like the one on which the following analyses are based always suffer from
some kind of limitations. Since the information was collected historically for quite different
reasons it is necessary to take a great deal of care over data preparation and selection (see also
Voland 2000a).
The basic sample of this study was restricted to families fulfilling the following criteria:
• The family reproductive history is completely known. That is, included families are those
for whom the start of the marriage is exactly known (wedding was recorded) as well as the
date of death of the spouse who died first (for this criterion see Voland and Dunbar 1995).
• The family was non-prosperous, i.e. it owned not more than 75 grasen of land (1 gras =
approx. 0.37 ha). The relatively prosperous farmer families owning 75 grasen and above
were excluded since, as we mentioned above, it is known that they manipulated the fates
of their children in accordance with the logic of a resource competition scenario while the
masses of workers dealt with their fertility “opportunistically” (Voland and Dunbar 1995;
Beise 2001).
• We only include first marriages for both husband and wife.
Furthermore, from these families only those children were selected
• who were born between 1720 and 1870,
• who were born alive,
• whose date of birth is precisely known,
• whose mothers survived the first five years of life of the child (in order to avoid
interfering effects by loss of the mother at an early age).
Naturally, this sample does not represent the general population - particularly because one
economic segment of the population was excluded (although for good reasons). Besides this,
the most prominent bias is that the more mobile segment of the population was excluded, too.
Since the precondition of being recorded in the data base is that any specific life-history event
had to take place in a geographically restricted area, this means that only children of families
could be considered that lived in this area for at least three generations. But since there is no
reason to detect how this could influence the two groups classified by the survival status of
the grandmothers in varying ways, this selection bias is ignored in the course of the following
analyses.
3 Methods
3.1 Event history modelsEvent history models were used to model the probability of death for the children over time.
These models are useful for analyses like this since first they account for the time dependency
of a process and second, they can easily cope with censored data. A transition rate model can
be represented mathematically by:
∑∑ ++=l
illk
ikki tzxtyt )()()(ln λβµ (1)
where )(ln tiµ is the log-hazard of occurrence of the event at time t for the ith child,
)(ty captures the baseline hazard, kx is the kth time constant covariate and lz is the lth time
varying covariate with β and λ as the respective regression parameters.
3.2 Single level vs. multilevelIn this study multilevel models will be applied (Goldstein 1997). The necessity of using
multilevel models is caused by the nested or hierarchical structure of the data. The data are
nested because the same family (or the same mother, which in this case is the same because
only one marriage per spouse was considered) could contribute several children to the
analysis. We assume that children from the same mother or the same family share many traits
which have an impact on their survival probability. This can be due to shared genetic effects,
social practices, and parental competence in basic childcare abilities (e.g. Das Gupta 1990;
Bolstad and Manda 2001). This dependence violates the assumption of independence of
observations which is required by traditional (single-level) statistical models. Intra-class
correlation can lead to misspecifications, because - for example - standard errors of
coefficients will be underestimated (for further details see Kreft and de Leeuw 1998:10 and
the literature cited therein). Multilevel models – by using the clustering information –
provides correct standard errors, confidence intervals and significance tests.
3.3 Unobserved heterogeneity A related but still different topic concerns the assumption of additional unobserved
heterogeneity in the data set. Family or woman specific characteristics other than those
considered as covariates may have an important influence on the mortality of the children.
These characteristics may contribute to individual knowledge or the ability to care for and
raise children, to aspects of the household which can result in a favorable or harmful
environment (like attitudes toward hygiene, commitment to children, etc.) or even to the
genetic make-up of parents and children. These characteristics are unobserved – either
because data about them are missing or because they are not measurable in principle. In order
to take those unobserved characteristics into account and control for their potential impact on
the outcome, a normally distributed random effect on the mother-level (with zero mean and
variance of sigma-square) was included in some of the models.
The software package aML 1.04 (Lillard and Panis 2000) was used to run all multilevel
models, the software package TDA 6.4a (Rohwer and Pötter 1999) was used to run a non-
parametric transition rate model.
3.4 Variables
This study focuses on the influence of grandmothers on the well-being or fitness of the
grandchildren. Since subtle fitness consequences for the children (physical or psychological
health, speed of development, etc.) are difficult or impossible to measure, the survival of the
children will serve as ultimate proxy for their fitness.
The probability of death was analyzed for the first 5 years of a child’s life. Children surviving
the first 60 months got censored at this age. This borderline is arbitrary in principle but was
chosen for a number of reasons: First, since the death of a child is the event under
observation, there should be enough events in order to get reasonable estimates. Human
mortality starts from a relatively high level just around birth (especially when in historical
populations or in developing countries) but then drops sharply just afterwards and reaches a
minimum during teenage time before it slowly increases again. Second, especially in those
sensitive ages with high mortality, (grandmaternal) support is most useful and may have a
significant impact. And third, especially in data bases of historical populations, many dates
are not exactly known, thus dates of death may actually have the form of a closed or even
open interval based on comparisons with other family-related dates. As a consequence, the
longer the observation time, the more cases that have to be excluded.
3.4.1 The grandmothers
The explanatory variables can be distinguished into explanatory variables in a literal sense
and those covariates which are included merely as a control function. The main focus in this
study is the potential grandmaternal impact.
Since we have no information about the quantity of support an individual grandparent
contributes to a child or its mother, the grandparent’s survival itself is used instead as a proxy.
The logic is that only a living grandparent is able to give support.
Grandmaternal survival entered different models both as a time-constant and as a time-
varying covariate. In the time-constant models, the survival status of the grandmother was
measured at the time of the birth of the child. In these cases no exact date of death (of the
grandmother) was necessary; instead a right censored situation was sufficient. Exact dates of
death for the grandmothers are needed when their survival status entered as time-varying
covariates. This decreased the sample size for those models slightly.
3.4.2 The grandfathers
In principle, the same conditions apply for the grandfathers as for the grandmothers.
Although the role of grandfathers is not explicitly taken into account in most of the theoretical
considerations so far (see for example Hawkes et al. 1998:1338, or Gurven and Hill 1997) the
grandfathers are included here for at least two reasons: First, as a kind of general control
variable in order to make sure that a potential finding of grandmaternal support is not the
result of grandpaternal influence. Second, the grandfather variable is included as a kind of
control variable in a more specific way: Since children have the same degree of relatedness to
their grandfathers as to their grandmothers (for the moment assuming that social relatedness
corresponds completely to biological relatedness) any difference in effects between the
survival of grandmothers and grandfathers on the effect of survival of their grandchildren
should reflect true behavioral causes and not potential genetic ones (ignoring here any
potential sex-linked effects in heritability, e.g. Cournil et al. 2000).
3.4.3 Age of mother
Age of mother is the most important control variable. It is well known that infant mortality is
tightly connected to the age of mother (McNamara 1982). When plotted as a graph, infant
death rates usually have a J-shape indicating a higher child mortality rate for very young
mothers and again a higher rate for advanced maternal ages of approximately 35 and older
(see for example Bolstad and Manda 2001: 17). In our context here it is particularly important
to control for the age of mothers because there is a direct dependency between our primary
covariate (grandmaternal survival) and the age of the mother: Younger mothers tend to have
younger grandmothers – or to put it another way: Children with living grandmothers have
younger mothers on average. Thus, children with living grandmothers should have on average
a higher probability of survival simply because their mothers are younger.
3.4.4 Cohort
This study covers an observation time for birth cohorts of children from 1720 to 1870. In
order to control for the uneven distribution of cases throughout this period and for differences
in mortality rates, 20 year cohorts are included as covariates. The cohorts enter as dummy
variables in order to account for non-linear dependencies.
3.4.5 Sex
The mortality of a child is effected by its sex in two ways. First, infant mortality is in general
higher among males than among females for physiological reasons (see references in
McNamara 1982). Second, some populations show a differential infant mortality rate
according to sex due to socio-cultural reasons. This is also true for the Krummhörn region
where the extent of differential mortality depends on membership in a socio-economic class
(Voland 1990).
3.4.6 Number of living siblings
Birth order effects on infant mortality are well-known in historical demography (e.g. Wrigley
and Schofield 1989; Lynch and Greenhouse 1994). In general, birth order and mortality are
positive correlated. The main reason may be a maternal heterogeneity in the ability to keep
children alive (e.g. Lynch and Greenhouse 1994). But family strategic reasons may also play a
role here since families may control their investment into a child’s well-being according to the
number of older siblings (e.g. Voland and Dunbar 1995). The number of living siblings is
used here instead of birth order since it can be assumed that the motivation of grandmothers to
help is more closely related to the actual family size than to the simple birth order.
3.4.7 Place of residence
The Krummhörn population showed mostly a patrilocal pattern (in relation to the parish of
residence) – although this pattern was by far not the only predominating appearance (Beise
2001). This variable entered as two dummy covariates indicating a shared parish of residence
of the children’s family with the maternal grandparents and the paternal ones, repectively. A
further dummy variable indicated missing information of the residence pattern. Note that the
children’s family can live in the same parish with one, both or neither member of the
grandparental pair. Furthermore, this variable indicates the residence irrespective of the
survival status of the grandparents.
Table 1 gives a short numerical overview of the explanatory variables and the outcome
variable.
TABLE 1 ABOUT HERE
4 Results
In the following models the nested structure of the data will be taken into account. This will
be done by applying a multilevel approach to the hazard models. Furthermore, since it can be
assumed that unobserved characteristics of mothers or families have an influence on child
mortality, unobserved heterogeneity will be added in some of the models. The analyses were
carried out using the special purpose software aML (Lillard and Panis 2000). This software
captures the baseline hazard )(ty in Equation (1) as a piecewise-linear spline (or generalized
Gompertz or piecewise linear Gompertz). The resulting parameter estimates of the baseline
can be understood as “slope parameters”. Knowing the starting point of the function (which in
this case is the intercept) and the nodes it is possible to graph the baseline spline using this
slope information. Such a graph is in fact the only sensible way of displaying the results for
interpretation. In the following section the results will be shown next to the tabled model
estimates. The estimates of the categorical covariates will be given as risks relative to the
baseline level (i.e. the anti-log of the estimated coefficients).
4.1 Grandparents’ survival as a time constant covariateThe first round of multilevel models will treat grandparental death as a set of time constant
covariates indicating the survival status at the time of birth of the child. In order to overcome
the proportionality assumption of the piecewise linear spline hazard model, an interaction is
run between the baseline and the grandmother covariates. The interaction makes the force of
mortality the form:
∑+−+=k
ijkkiiij xtyztyzt βµ )()1()()(ln 21 (2)
where zi is a (binary) covariate representing the grandmaternal survival status at the time of
the child’s birth (z=1 if dead and z=0 if alive). The remaining terms are the same as in
Equation 1. Such a model effectively estimates two different baselines: y1(t) captures the
baseline hazard for children with grandmothers alive at the time of their birth and y2(t)
captures the baseline hazard for those whose grandmothers were already dead.
Table 2 summarizes the results of this model. The interaction of the survival status of the
maternal and paternal grandmothers with the baseline hazard are estimated in separate
models. The respective non interacting grandmother variable enters as a simple time constant
variable in the model. For every interaction two models are estimated, namely (i) one stripped
down model which beside the interacting grandmother indicator only includes one other
covariate, namely the remaining grandmother and (ii) a second – full – model with all the
covariates included. The baseline of the models are graphed in figure 2.
[TABLE 2 ABOUT HERE]
[FIGURE 2 ABOUT HERE]
The graphs in figure 2 show the typical shape of the mortality hazard for children, i.e. a very
high mortality right after birth and a very fast decrease followed by a stability at a relatively
low level after approximately the age of three. Since the full models hardly differ from the
stripped-down models the following description refers to both kinds of models.
Comparing the baseline hazards for children whose grandmothers were alive at their birth and
children whose grandmothers were dead, two distinct differences can be noticed: First, while
a dead maternal grandmother increased the grandchild’s hazard to die, a dead paternal
grandmother decreased the hazard. Or to put it in relation to a positive survival status of the
grandmother: If the maternal grandmother was alive, a child was less likely to die than if she
was dead. The opposite was true for a paternal grandmother: If she was alive the probability
of the child dying was higher. Second, the differences in the baseline hazards between living
and dead grandmothers became evident at different ages for the two grandmothers. For
maternal grandmothers, there was no difference in the hazards right after birth. The hazards
start to diverge around one month after birth and are especially pronounced between the ages
of 6 months and 2 years. For paternal grandmothers the biggest difference appears right after
birth. There is almost no difference in the hazards between the ages of 1 month and 12
months, then there is again a difference around the age of 2 years.
The contrasting effects of the grandmaternal impacts are also obvious from the relative risks
in table 1, although the effects are not always significant. While a dead paternal grandmother
decreased the relative risk for her grandchild to die by 10% or 17% (for models 1 and 2,
respectively), a dead maternal grandmother increased the relative risk by 14% or 18%
(models 3 and 4, respectively). Furthermore, it should be noted that both maternal and
paternal grandfathers have virtually no effect on the mortality of their grandchildren.
Also, there is no effect from the number of living siblings, the age of the mother or from the
sex of the child (though girls seem to fare somewhat better than boys, as expected). For
missing values of the age of the mother (due to missing maternal date of birth), a separate
dummy variable was included in the model. The effect of this covariate is highly significant,
though it is not clear in which way this selection for higher mortality worked.
The birth cohort also had a significant influence on the estimated mortality hazards. Cohorts
born before 1840 had a higher mortality (even increasing with increasing temporal distance)
than the subsequent cohort, born between 1840 and 1869. Only the very first birth cohort
showed a mortality opposing this trend. This could be a hint for an under-registration of death
in this early period.
And finally another effect is puzzling: A matrilocal residence pattern increased significantly
the children’s mortality while a patrilocal decreased it (though this effect is not significant).
This means (controlling for the grandpaternal survival status) that a matrilocal residence was
inferior for the survival of the children – especially compared to patrilocal residence.
4.2 Grandparents’ survival as a time varying covariateIn the next models, grandparental deaths enter as time-varying covariates. This takes into
account that grandparents may have survived the birth of their grandchild but died sometime
later during the observation period of the first five years. This model design is therefore
probably the most accurate one, although the sample size decreased slightly compared to the
previous models, since now only cases with exact information about the grandparental death
could be considered (while in the previous models it was sufficient to know if the grandparent
died sometime before the date of birth of the child – in historical data sets, this kind of
information is not rare). Again the model was specified in a way that the time-varying
covariate ‘grandmaternal death’ interacts with the baseline. This was solved by defining in
addition to the baseline hazard a second time dependent linear spline term which enters
conditionally on the event that the grandmother dies. This term then additively changes the
baseline hazard. The mathematical representation can be written as follows:
jl
illk
ijkkiiij Utzxdtcztyt +++−+= ∑∑ )()()()(ln λβµ (3)
where zi is a similar binary covariate like in equation 2 (indicating if a specific grandparent is
dead or not at a specific point in time) and c(t-di) is a time dependent linear spline term which
enters the model only if the grandparent is dead. This “correction” term represents the effect
of the dead grandparent on the mortality hazard with di indicating the time of death of the
grandmother concerned (relative to the age of the child). In addition, this equation includes a
random effect term Uj which captures potential unobserved heterogeneity at the mother level.
Again, this model is estimated for every grandmother separately. For each grandmother, two
full models are estimated, differing only in the random effect term which is included just
once. The results are listed in table 3 and the estimated baselines are graphed in figure 3.
[TABLE 3 ABOUT HERE]
[FIGURE 3 ABOUT HERE]
Due to the modified specification of the model presented above, the plotting of the baseline
(figure 3) differs from that of the previous models. The basic baseline represents the hazards
for children with a living grandmother. The effect of having a dead grandmother enters the
model as an extra term at the time point (in the child’s life) when she dies. This means, in
order to get a graph of the hazards for children with a dead grandmother it is necessary to add
a graph of the additional effect (of a dead grandmother) to the graph for children with living
grandmothers. These three graphs are depicted in each diagram. The upper row of panels
shows the baselines for the models without unobserved heterogeneity, the lower row the
baselines for the models including unobserved heterogeneity.
The baseline hazards look almost identical to the ones we found when we treated
grandmaternal survival as time constant covariates. Also, the relative risks of the control
variables (table 3) are very similar to those from the previous full model, but especially the
effect of the maternal grandmother’s survival sharpened further and is now significant at the
������ ��������� ���� ��� ������������ ���� ���� �������� ����� ����������������������� ���
children without a living maternal grandmother than for children with a living grandmother.
But since we are less interested in the shape of the mortality curves itself but in the relative
difference in the hazards between the two groups of children, it is actually more useful to
display the ratio of the hazards. Figure 4 shows the ratio of the mortality hazard for children
without a living grandmother to the hazard of children with a living grandmother. The ratios
are calculated for age intervals by using the anti-log of the log-hazards and after conversion of
the linear splines into average hazards for these age intervals. The graph is scaled to a
balanced ratio. Every box rising above the 0-baseline indicates an increased mortality for
children without the relevant grandmother; every box below this line indicates a lower
mortality. The ratios for maternal and paternal grandmothers are combined into one plot.
Figure 4 shows very clearly that the increase in the force of mortality of children with a living
paternal grandmother is especially strong in the very first month of life. A smaller but
concurrent effect can be seen in the second and third year of life. The mortality decrease
associated with a living maternal grandmother is highest in the second half of the child’s first
year and in the two surrounding age classes.
[FIGURE 4 ABOUT HERE]
The results in table 3 show a large standard deviation of the random effect, which is highly
significant. This indicates a large amount of unobserved heterogeneity among the mothers of
this sample which can be interpreted in a way that mothers varied systematically in their
ability to keep their children alive – no matter whether this ability was based on genetic,
behavioral, socioeconomic or any other differences. But this heterogeneity did not influence
either the effect of the main explanatory variables (the grandmother’s survival status) or the
effects of the other control variables. None of these variables changed substantially their
estimated coefficients when unobserved heterogeneity was taken into account.
5 Discussion
Two main results emerge from this study. First, in accordance with the expectations of the
“grandmother hypothesis” grandmothers in the Krummhörn of the 18th and 19th century may
indeed improved the survival of their grandchildren. Referring to the maternal grandmother,
the odds increased by up to 23% over the first 5 years of the child’s life (table 3). Second, this
effect was limited to the maternal grandmothers while having a living paternal grandmother
was even more harmful for a child than having none: When the paternal grandmother was
alive the odds of surviving decreased by up to 19% (table 3).
But the effects of the two grandmothers differed not only concerning the direction of the
impact but also concerning the timing of these effects (figure 4). Children without a living
maternal grandmother had a higher mortality risk especially between the ages of 6 and 12
months (60% higher!), a risk which started already after one month of life and was elevated
still during the second year. By contrast, the substantial – and opposite – effect of the paternal
grandmother was almost exclusively evident in the very first month of life: In this month the
average hazard for children with a dead paternal grandmother was over 40% lower than the
hazard of children with this grandmother alive.
It is important to note this temporal pattern since it gives hints concerning the mechanisms at
work. Infant deaths can be separated into two broad categories according to causation. Death
may have an exogenous cause, like infectious and parasitic diseases, accidents, or other
external causes. Or death may be caused endogenously, as a result of congenital
malformations, conditions of prenatal life, or the birth process itself. Exogenous causes
predominate all deaths after the first month of life while deaths in the first weeks after birth
are mainly the result of endogenous causes (McNamara 1982). Thus, the specific effect of the
paternal grandmother just in the very first month could be a hint that her impairing influence
was not directed towards the child itself but instead worked by effecting the living conditions
of the wife during pregnancy. In comparison, no effect of the maternal grandmother could be
found at this age. Her beneficial effect started only after the first month and was highest
during the second half of the first year, at a time when mortality is in general dominated by
exogenous causes.
The effect of external help on the survival of the new-born child depends on two aspects
which can be framed in the following questions: First, when is support most needed? And
second, when can support effectively influence the children’s survival? Support should have
the greatest effect when mortality is highest, because then many lives can be saved. Since
mortality is highest just after birth, this age should be the most appropriate time to give
support. But due to the dominating endogenous causes there is almost no possibility to
influence survival beneficially. After the first month of life the possibilities for grandmothers
to contribute to the survival of their grandchildren increase to the same extent as the
importance of endogenous factors in infant mortality decreases. But still, as long as the
mother is breast-feeding, the possibilities remain limited. A second mortality crisis for
children occurs at the time of weaning (McNamara 1982). In the Krummhörn, this took place
on average after about 10 months (Kaiser 1998:27). After weaning, mortality declines further
and by then the child can be more or less fully independent of the mother if it gets substantial
support by others.
Interestingly, the time pattern of the maternal grandmother effect reflects this interrelation
between the need of support and the effectiveness of support quite precisely: There is no
effect of the survival of the maternal grandmother in the very first month, there is some effect
for the rest of the first half year of life, and there is the strongest effect in the second half of
the first year, when the child is very vulnerable due to weaning (and at the same time lose the
exclusive dependence on the mother).
The picture for the paternal grandmother looks very different. The higher mortality in the first
month is a hint that the paternal grandmother’s influence – although it appears only after the
birth of the child – actually took place during the pregnancy. This finding could reflect what is
known both popularly as the “evil mother-in-law” and in psychological research as the
varying closeness in relationships of family members (Euler et al. 2001). It is the relationship
between wives and their mothers-in-law which is supposed to be especially tension-loaded –
even with potentially long lasting effects. In a study of a Japanese village, Skinner (1997:77)
found that an early death of the mother-in-law increased the wife’s longevity. But what is the
reason for this special relationship and the differences in investment conditional on whether
the grandchild belongs to a son or a daughter?
Ultimately it may be traced back to “paternity uncertainty”, a phenomenon which is
responsible for a wide range of behavioral traits in humans and animals (Clutton-Brock 1991;
Daly et al. 1993). While women can always be sure about their biological relatedness to their
children, men can not. The consequence is that the maternal grandmother is the only one
among the grandparents who can be completely sure about the relatedness to her
grandchildren. If investments in children are given according to the degree of certainty about
relatedness, patrilineal relatives should be less willing to give support than matrilineal
relatives (Alexander 1974). This insecurity about the wife’s fidelity could give rise to some
social conflict between the patrilineal relatives and the mother who married into the family in
which the postreproductive mother of the son is especially prone to active participation.
Fitting to these considerations is a study by Euler and Weizel (1996) which found in a
psychological analysis of grandparental solicitude an ordered pattern in which the maternal
grandmother contributes most care and the paternal grandfather the least care. Still, it is
difficult to estimate the significance of this aspect for the Krummhörn population, especially
since the cultural background was predominated by a strong calvinistic belief which made it
unlikely that uncertainty about paternity was very high (although precisely this could be the
result of a restrictive domestic environment). Thus, this line of argumentation remains very
speculative without further knowledge about the socio-cultural setting and the contemporary
mentality in the Krummhörn population.
A frequent critique related to the empirical testing of the grandmother hypothesis is what may
be interpreted as a beneficial grandmaternal effect is actually the result of genetic inheritance
of something like robustness (or frailty). The idea behind this critique is that healthy and long
living grandmothers also have healthy and robust grandchildren. A very similar critique is
directed against explanations of a correlation with the sharing of a beneficial family
environment. Neither of these critiques seems to apply here: First, beside the positive
correlation between the survival of the grandmother and the grandchildren, we also found a
negative one which contradicts the assumption of the operation of a common background
variable. Second, although grandmothers and grandfathers shared almost identical
environments for a large part of their life and although they share (on average) an equal
amount of genetic material with their grandchildren, the effects of the survival status of
grandmothers and grandfathers differed considerably. While there was a substantial effect for
the grandmothers, there was almost no effect for the grandfathers – a result that parallels the
finding of Sear and colleagues (2000, 2002) for a current population in rural Gambia.
To sum up, this study – going technically beyond what was done in Voland and Beise (2002)
– found a significant beneficial effect of the maternal grandmother. This effect proved to be
very stable (considering the control for dependency of events between children of the same
mother and the control for unobserved heterogeneity) and is unique among all the
grandparents. It is furthermore in accordance with the expectations of the grandmother
hypothesis and its follow-ups which emphasize the importance especially of the matrilineal
kin (Hawkes et al. 1998). Our findings give support to the idea that women can improve their
inclusive fitness substantially even after cessation of their reproductive capabilities (and after
their own children grew into adulthood) – and that such a trait can be observed even in a
modern, though historic, European population. On the other hand, the opposite, harmful effect
of the paternal grandmother – although stable as well – needs some further investigations.
This effect could fit into a scenario of differing reproductive strategies according to
matrilineal or patrilineal descent, but such an explanation is still very speculative. Further
comparative studies on populations of differing family systems and values could offer greater
clarification.
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Table 1: Statistical description of the sample and the variables on which the following analyses are based.
Baseline Number ofcases at risk
Number ofevents
Total 3550 659
Age intervals1
0-1 month 3530 1701-6 months 3360 1206-12 months 3240 6912-24 months 3171 12124-36 months 3050 7736-60 months 2973 77
Covariates Number ofcases
Number ofevents
maternal grandmother2
alive 1777 313dead 1753 346
paternal grandmother2
alive 1613 315dead 1917 344
maternal grandfather2
alive 1440 260dead 1822 352missing 268 47
paternal grandfather2
alive 1159 229dead 2131 385missing 240 45
sexmale 1783 339female 1747 320
age of mother15-25 yrs. 504 10025-35 yrs. 1921 35435-50 yrs. 992 176missing 113 29
birth cohort1720-1749 102 191750-1779 526 1281780-1809 840 1871810-1839 1407 2421840-69 655 83
number of siblings0 868 1591-2 1506 3013+ 1156 199
place of residence3
matrilocal 1609 342patrilocal 2362 431missing 161 25
1 Age intervals inclusive the left border and exclusive the right border2 Survival status at the time of birth of the child3 Note that the residence indication refers to the parish level, i.e. following this definition a family can be at thesame time matrilocal and patrilocal (see text).
Figure 1: Kaplan-Meier survival curves classified by the constellation of the grandmother’s survivalstatus (at the time of birth of the child), modified from Voland and Beise 2002.
Table 2: Interaction with the baseline of the grandmother’s survival status as a time constant variable (note: gm = grandmother, gf = grandfather).
Maternal grandmother Paternal grandmotherModel 1 Model 2 Model 3 Model 4
Baseline (Age of Child) b b b b b b b balive dead alive dead alive dead alive dead
Intercept -2.0510 ** -2.0729 ** -2.2676 ** -2.3538 ** -1.8878 ** -2.5011 ** -2.1599 ** -2.8618 **1 month -2.1797 ** -1.9819 ** -2.4463 ** -1.9642 ** -2.4594 ** -1.7060 ** -2.5258 ** -1.8155 **6 months -0.3502 ** -0.3162 ** -0.3060 ** -0.3304 ** -0.3267 ** -0.3350 ** -0.3137 ** -0.3271 **12 months 0.0297 0.0715 0.0116 0.0711 0.0476 0.0589 0.0278 0.061624 months 0.0007 -0.0609 * 0.0058 -0.0643 * -0.0005 -0.0639 * 0.0052 -0.0696 *36 months -0.0557 * -0.0335 -0.0512 + -0.0292 -0.0733 ** -0.0157 -0.0758 ** -0.003060 months 0.0020 -0.0133 -0.0028 -0.0054 -0.0054 -0.0055 -0.0078 -0.0024
Covariates relative risk relative risk relative risk relative riskmaternal gm (alive)
dead 1.14 + 1.18 +paternal gm (alive)
dead 0.90 0.83 *maternal gf (alive)
dead 1.08 1.08paternal gf (alive)
dead 0.97 0.97sex (male)
female 0.94 0.94age of mother (25-35 yrs.)
15-25 yrs. 1.02 1.0235-50 yrs. 0.99 0.99missing information 1.95 ** 1.96 **
birth cohort (1840-69)1720-1749 1.44 1.441750-1779 1.82 ** 1.81 **1780-1809 1.75 ** 1.75 **1810-1839 1.30 + 1.31 +
number of siblings (0)1-2 1.15 1.153+ 0.92 0.92
place of residence1
matrilocal 1.20 * 1.20 *patrilocal 0.88 0.88missing information 0.84 0.84
N 3530 3043 3530 3043Khgm07d2 khgm07d khgm07e2 khgm07e
Note: + p<0.1; * p<0.05; ** p<0.01
1 Note that the residence indication refers to the parish level, i.e. following this definition a family can be at the same time matrilocal and patrilocal (see text).
Figure 2: Baseline hazard for models 1 to 4 (models estimating an interaction with the baseline ofgrandmaternal survival status as a time constant covariate). The upper panels show the baselines ofthe stripped-down models while the lower panels show the baselines of the full models (note: mm =maternal grandmother [mother’s mother], fm = paternal grandmother [father’s mother]).
Maternal grandmother (Model 1)
-8.00
-7.00
-6.00
-5.00
-4.00
-3.00
-2.00
-1.00
0.00
0 12 24 36 48 60
Age of child [months]
log
inte
nsi
ty
mm alivemm dead
Maternal grandmother (Model 2)
-8.00
-7.00
-6.00
-5.00
-4.00
-3.00
-2.00
-1.00
0.00
0 12 24 36 48 60
Age of child [months]
log
inte
nsi
ty
mm alivemm dead
Paternal grandmother (Model 3)
-8.00
-7.00
-6.00
-5.00
-4.00
-3.00
-2.00
-1.00
0.00
0 12 24 36 48 60
Age of child [months]
log
inte
nsi
ty
fm alivefm dead
Paternal grandmother (Model 4)
-8.00
-7.00
-6.00
-5.00
-4.00
-3.00
-2.00
-1.00
0.00
0 12 24 36 48 60
Age of child [months]
log
inte
nsi
ty
fm alivefm dead
Table 3: Interaction with the baseline of grandmother’s survival status as a time varying variable.
Maternal grandmother Paternal grandmotherModel 5 Model 6 Model 7 Model 8
Baseline (Age of child) b B b bGrandmother alive
Intercept -2.2577 ** -2.2407 ** -2.1598 ** -2.1520 **1 month -2.4423 ** -2.4343 ** -2.5273 ** -2.5151 **6 months -0.3073 ** -0.3044 ** -0.3138 ** -0.3124 **12 months 0.0137 0.0123 0.0276 0.027524 months 0.0048 0.0061 0.0046 0.005636 months -0.0501 + -0.0503 + -0.0760 ** -0.0763 **60 months -0.0021 -0.0018 -0.0082 -0.0076
Difference of deadgrandmother
Intercept -0.0806 -0.0920 -0.7093 ** -0.7226 **1 month 0.4792 0.4755 0.7154 * 0.7042 *6 months -0.0231 -0.0236 -0.0142 -0.013012 months 0.0580 0.0602 0.0345 0.035424 months -0.0690 -0.0692 -0.0751 + -0.0753 +36 months 0.0215 0.0216 0.0728 + 0.0731 +60 months -0.0032 -0.0033 0.0056 0.0052
Covariates relative risk relative risk relative risk relative riskmaternal gm (alive)
dead 1.23 * 1.22 *paternal gm (alive)
dead 0.83 * 0.81 *maternal gf (alive)
dead 1.00 1.00 1.00 1.00paternal gf (alive)
dead 1.01 1.01 1.01 1.01sex (male)
female 0.93 0.93 0.94 0.93age of mother (25-35 yrs.)
15-25 yrs. 1.02 1.02 1.03 1.0235-50 yrs. 1.00 0.97 0.99 0.96missing information 1.94 ** 2.00 ** 1.94 ** 1.99 *
birth cohort (1840-69)1720-1749 1.42 1.47 1.43 1.471750-1779 1.81 ** 1.83 ** 1.81 ** 1.82 **1780-1809 1.76 ** 1.78 ** 1.75 ** 1.77 **1810-1839 1.30 + 1.30 + 1.29 + 1.30 +
number of siblings (0)1-2 1.15 1.13 1.15 1.143+ 0.92 0.84 0.92 0.85
place of residence1
matrilocal 1.20 * 1.20 * 1.20 * 1.20 *patrilocal 0.89 0.89 0.89 0.89missing information 0.85 0.83 0.85 0.83
Unobserv. HeterogeneitySigma 0.4213 ** 0.4165 **
N 3043 3043 3043 3043khgm08d khgm08dd khgm08e khgm08ee
Note: + p<0.1; * p<0.05; ** p<0.01
1 Note that the residence indication refers to the parish level, i.e. following this definition a family can be atthe same time matrilocal and patrilocal (see text).
Figure 3: Baseline hazards for models 5 to 8 (models with an interaction with the baseline of thegrandmaternal survival status as a time varying covariate). The upper panels show the baseline forthe full models without heterogeneity, the lower panels the baselines for models including unobservedheterogeneity (Note: mm = maternal grandmother, fm = paternal grandmother).
Maternal grandmother (Model 5)
-8.00
-7.00
-6.00
-5.00
-4.00
-3.00
-2.00
-1.00
0.00
1.00
0 12 24 36 48 60
Age of child [months]
log
inte
nsi
ty mm alivemm deadeffect dead
Paternal grandmother (Model 6)
-8.00
-7.00
-6.00
-5.00
-4.00
-3.00
-2.00
-1.00
0.00
1.00
0 12 24 36 48 60
Age of child [months]
log
inte
nsi
ty fm alivefm deadeffect dead
Maternal grandmother (Model 7)
-8.00
-7.00
-6.00
-5.00
-4.00
-3.00
-2.00
-1.00
0.00
1.00
0 12 24 36 48 60
Age of child [months]
log
inte
nsi
ty mm alivemm deadeffect dead
Paternal grandmother (Model 8)
-8.00
-7.00
-6.00
-5.00
-4.00
-3.00
-2.00
-1.00
0.00
1.00
0 12 24 36 48 60
Age of child [months]
log
inte
nsi
ty fm alivefm deadeffect dead
Figure 4: Mortality hazard of children without a living grandmother relative to those with a livinggrandmother (age intervals inclusive the left border and exclusive the right border).
0.20
0.40
0.60
0.80
1.00
1.20
1.40
1.60
1.80
0-1 1-6 6-12 12-24 24-36 36-60
Age of child [months]
Haz
ard
rat
io (
dea
d g
m/li
vin
g g
m)
maternal gmpaternal gm
